二阶差分方程xn+1=a/xn2+1/xn-1 的全局渐近稳定性
Global Asymptotic Stability of the Second-Order Nonlinear Difference Equation xn+1=a/xn2+1/xn-1
DOI: 10.12677/PM.2017.71003, PDF, HTML, XML, 下载: 1,536  浏览: 3,592 
作者: 秦旭光*, 冯 伟：北京航空航天大学数学与系统科学学院，北京
关键词: 全局渐近稳定；二周期解；平衡点；Global Asymptotic Stability； Period-2 Solution； Equilibrium
摘要: 本文研究了非线性差分方程xn+1=a/xn2+1/xn-1 ，当参数a∈(0，∞) ，初值满足x-1，x0∈(0，∞)时的全局渐近稳定性。我们给出了方程的正平衡点和二周期解都不具有全局渐近稳定性的结论。特别的，解决了V. L. Kocic和G. Ladas著作[1]中的一个公开问题，部分解决了另一个公开问题。
Abstract: In this paper the global asymptotic stability of nonlinear difference equation xn+1=a/xn2+1/xn-1 is investigated, where a and the initial conditions x-1，x0 are positive real numbers. We show that both of the unique positive equilibrium and the unique period-2 solution are not globally asymptotically stable. In particular, our results solve one open problem proposed by V. L. Kocic and G. Ladas in monograph [1], and partly solve another open problem proposed by them.
文章引用：秦旭光, 冯伟. 二阶差分方程xn+1=a/xn2+1/xn-1 的全局渐近稳定性[J]. 理论数学, 2017, 7(1): 16-19. http://dx.doi.org/10.12677/PM.2017.71003

参考文献

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